Toronto Math Forum
MAT2442018F => MAT244Tests => Quiz5 => Topic started by: Victor Ivrii on November 02, 2018, 03:14:52 PM

Use the method of variation of parameters (without reducing an order) to determine the general solution of the given differential equation:
$$
y''' + y' = \tan (t),\qquad \pi /2 < t < \pi /2.
$$

Answer is in the attachment.

Hi Guanyao Liang,
Your answer is very close, but I think you messed up a calculation. The integral of $\tan(t)$ is $\ln\cos(t)$, not $\ln\sec(t)$.
Therefore the solution should be:
$y = c_1 + c_2\cos(t) + c_3\sin(t)  \ln\cos(t)  \sin(t)\ln\sec(t) + \tan(t)$

Hi Guanyao Liang,
Your answer is very close, but I think you messed up a calculation. The integral of $\tan(t)$ is $\ln\cos(t)$, not $\ln\sec(t)$.
Therefore the solution should be:
$y = c_1 + c_2\cos(t) + c_3\sin(t)  \ln\cos(t)  \sin(t)\ln\sec(t) + \tan(t)$
Hi Michael, $\ln{sec(t)} and \ln{cos(t)}$ are the same thing... :)

oh right! Totally my bad! time to relearn trig.. :\